Method for regulating the temperature of a metal strip, especially for rolling a metal hot trip in a finishing train

ABSTRACT

The invention relates to a method for controlling and regulating the temperature of a metal strip in a finishing train of a hot rolling mill. A target function is formed by comparing a desired temperature gradient with an actual temperature gradient. The target function measures deviations from desired indications positioned in various places on the finishing train. The speed of the strip and the flow of the cooling agent are adjusted by predicting with the aid of a method of non-linear optimization with auxiliary conditions and are regulated and controlled online by solving a quadratic optimization problem with linear auxiliary conditions, preferably with the aid of an active set strategy.

CROSS REFERENCE TO RELATED APPLICATIONS

This application claims priority to the German applicationsNo.10308222.0, filed Feb. 25, 2003 and No.10321791.6, filed May 14,2003, and to the International Application No. PCT/EP2004/001366, filedFeb. 13, 2004 which are incorporated by reference herein in theirentirety.

FIELD OF INVENTION

The invention relates to a method for controlling and regulating thetemperature of a metal strip, e.g. of steel or aluminum, in a finishingtrain for rolling a metal hot strip.

BACKGROUND OF INVENTION

U.S. Pat. No. 6,220,067 B1 describes a method which regulates thetemperature of a metal strip at the output end of a mill train, i.e. thefinal rolling temperature. A method of this type cannot adequatelyselectively influence phase changes, which especially in dual-phaserolling are of significance for the material properties of the rolledmetal strip, in the steel in the mill train. A comparable method, whichserves for calculating a pass schedule, is described in EP 1 014 239 A1.

SUMMARY OF INVENTION

The material properties and the structure of a rolled metal strip aredetermined by chemical composition and process parameters, especiallyduring the rolling process, such as e.g. load distribution andtemperature management. Final control elements for the rollingtemperature, in particular the final rolling temperature, are, dependingon the type of plant and mode of operation, generally speed of the stripand inter-stand cooling.

An object of the invention is to improve the control or regulation ofthe temperature of a metal strip, especially in a finishing train, suchthat disadvantages known from the prior art are avoided and inparticular that the control or regulation of the aforementioned finalcontrol elements is improved.

The object according to the invention is achieved in a method forcontrolling and/or regulating the temperature of a metal strip,especially in a finishing train, whereby, in order to determineadjustment signals, a desired temperature gradient is compared with anactual temperature gradient, whereby a temperature gradient forindividual strip points on the metal strip is determined and whereby,taking into account auxiliary conditions, at least one target functionis formed for final control elements of the plant in the finishingtrain.

In determining the temperature gradient for individual points on thestrip, the path and preferably also properties such as the temperatureof individual points on the strip are advantageously traced. In thisway, the precision of the control and regulation is significantlyimproved.

Advantageously, the target function is solved by solving an optimizationproblem. Here, technical constraints such as in particular adjustmentlimitations of the final control elements are taken into account in anextremely favorable manner whereby, in particular, as much scope aspossible is provided for changing the final control elements and wherebythe computing time needed for controlling and regulating is kept verylow.

Advantageously, a desired temperature at the end of the finishing trainis predetermined. Alternatively, or in addition, at least one desiredtemperature in the finishing train is predetermined. Control andregulation are in this way substantially improved with regard to thematerial properties of the metal strip and with regard to its structuralcomposition.

Advantageously, the actual temperature gradient of the metal strip isdetermined with the aid of at least one model. In this way, improvedcontrol or regulation of the temperature of the metal strip is enabled,even if the actual temperature of the strip cannot be measured atpoints, especially in the finishing train, relevant for control orregulation.

Advantageously, the model is adapted online. In this way, any plantdrift that exists can be taken into account and realistic results,especially for the next metal strips to be rolled, can be determined.

Advantageously, adjustment signals are determined for the flow of thecooling agent.

Advantageously, actuating signals are determined for the flow of thematerial.

Advantageously, in order to solve the target function, an optimizationproblem with linear auxiliary conditions is solved online, i.e. inparticular in real time. Adjustment limitations are established here, inparticular in the form of equality or inequality auxiliary conditions.Solution of the optimization advantageously returns here the values ofthe adjustment variables for a next controller cycle. This providesregulation that is structured clearly, uniformly and independently ofthe plant configuration and that works reliably and fast.

Advantageously, a quadratic optimization problem is solved. Theoptimization problem can in this way be solved particularly fast.

Advantageously, the optimization problem is solved with the aid of anactive set strategy. The optimization problem can in this way be solvedparticularly effectively in real time.

Advantageously, an online-capable pass schedule algorithm is calculatedin advance by means of non-linear optimizations with auxiliaryconditions. The length of time for calculating the pass schedule is inthis way kept extremely small. The calculation of the pass schedulereturns set-up values which are in particular optimally matched to thecontroller operating online. In this way the controller has sufficientscope to influence the temperature of the strip.

The inventive method for controlling and for regulating the temperatureof a metal strip is in particular also suitable for rolling strips witha thickness wedge, as is used for example in semi-continuous rollingwith finished strip thicknesses below 1 mm. When rolling strips with athickness wedge, additional auxiliary conditions with regard to thefinal control elements become active.

Further embodiments are included in the remaining independent anddependent claims. The advantages described for the method according tothe invention apply analogously.

BRIEF DESCRIPTION OF THE DRAWINGS

Further advantages and details will emerge from the description below ofseveral exemplary embodiments of the invention and from the associateddrawings in which by way of example:

FIG. 1 shows the basic structure of a rolling mill,

FIG. 2 shows the schematic arrangement of a model-predictive control forthe finishing train,

FIG. 3 shows a schematic representation relating to the model-predictivecontrol,

FIG. 4 shows the adjustment or prediction horizon for the flow of thecooling agent, and

FIG. 5 shows the adjustment or prediction horizon for the flow of thematerial.

DETAILED DESCRIPTION OF INVENTION

FIG. 1 shows a plant for the production of metal strip 6, comprising aroughing train 2, a finishing train 3 and a cooling stretch 4. Plants ofthis type are typical for the steel and metal industry. A reeling device5 is arranged downstream of the cooling stretch 4. The metal strip 6which is rolled preferably hot in the trains 2 and 3 and cooled in thecooling stretch 4 is reeled in by said reeling device. A strip source 1is arranged upstream of the trains 2 and 3, which strip source isfashioned for example as a furnace in which metal slabs are heated orfor example as a continuous casting plant in which metal strip 6 isproduced. The metal strip 6 consists for example of aluminum or steel.

The plant and in particular the trains 2, 3 and the cooling stretch 4and the at least one reeling device 5 are controlled by means of acontrol method which is executed by a computing device 13. To this end,the computing device 13 has control engineering links to the individualcomponents 1 to 5 of the plant for steel or aluminum production. Thecomputing device 13 is programmed with a control program fashioned as acomputer program, on the basis of which it executes the method accordingto the invention for controlling and regulating the temperature of themetal strip 6.

In accordance with FIG. 1, the metal strip or slab 6 leaves the stripsource 1 and is then first rolled in the roughing train 2 to an inputthickness for the finishing train 3. Inside the finishing train, thestrip 6 is then rolled by means of the rolling stands 3′ to its finalthickness. The subsequent cooling stretch 4 cools the strip 6 to apredetermined reeling temperature.

In order to ensure desired mechanical properties in the strip 6, asuitable temperature gradient has to be observed for the finishing train3 and the cooling stretch 4. Since virtually no widening of the rolledstrip 6 occurs during the rolling process, the length of the stripand—provided the flow of material remains constant—the speed of thestrip increase through the rolling process.

FIG. 2 presents in detail the finishing train 3 with its rolling stands3′ and illustrates the model-predictive regulation of the finishingtrain 3 according to the invention.

Inside the finishing train 3, the times of contact of the hot metalstrip 6 with the relatively cold working rolls of the rolling stands 3′and the inter-stand cooling devices 7 are the most important factorsinfluencing the temperature of the metal strip 6. The final controlelements for controlling and regulating the temperature of the strip inthe finishing train are accordingly the flow of the material 16 and theflow of the cooling agent 8. In FIG. 2, two strip points P₀, P₁ on themetal strip 6 are highlighted by way of example in order to simplify theexplanation of the exemplary embodiment.

The finishing train 3 is delimited by its start x_(A) and its end x_(E).The plant dynamics in the finishing train 3 are characterized in termsof temperature by relatively long idle times 105. Thus, for example, theinfluence of a change in the flow of the cooling agent 8 on thetemperature at the end x_(A) of the finishing train 3 can be observedonly when the first strip point P₀, P₁ which was influenced by thischange leaves the last rolling stand 3′. That is one reason whyregulation of the strip temperature 17 according to the invention isfashioned as model-predictive regulation.

The computing device 13 for controlling the steel industry plant and inparticular for controlling the finishing train 3 has a strip temperaturemodel 12 and a strip temperature regulation 17. The strip temperaturemodel 12 and the strip temperature regulation 17 operate preferablycyclically in regulating steps.

The strip temperature regulation 17 has a regulating device 14 whichcontrols and regulates the flow of the cooling agent 14 of theinter-stand cooling devices 7 and the flow of the material 16 of themetal strip 6, i.e. in particular the speed v of said metal strip.Upstream of the regulating device 14 is a linearized model 15 which isprocessed with the aid of quadratic programming.

The module 12 for determining the strip temperature online has an onlinemonitor 9 for ascertaining the current strip temperature, a module foronline adaptation 10 and preferably a module for predicting 11 thetemperature T^(j) _(k=0,1) of selected points P₀, P₁ on the strip.

The online monitor 9 uses a model for determining the current striptemperature and preferably the phase status of the metal strip 6 insidethe finishing train 3. The module 12 for determining the striptemperature online therefore has a strip temperature model, not shown indetail in the drawings. The strip temperature model makes it possiblefor example to predict the final temperature of strip points P ₀, P₁,i.e. in particular the temperature of the strip points P0, P1, at theposition x_(E). Taking this as a starting point, a linearized model 15is set up which determines the strip temperature for a working point ofthe finishing train 3 for a given change in the flow of the coolingagent 8 and/or a given change in the flow of the material 16.

By minimizing the quadratic deviation of the output of the linearizedmodel 15, new correction values are determined for flow of the coolingagent 8 and flow of the material 16. Given desired values for interimstrip temperatures preferably inside the finishing train or givendesired values for the final temperature of the strip 6 in the finishingtrain 3 are taken into account in determining these correction values.Through linearization of the strip temperature model, a quadraticprogramming problem is produced which can be solved sufficiently fast toallow online control of the strip temperature.

The task of the online monitor 9 is to determine the current status,i.e. in particular all the interim temperatures needed for control andregulation, of the metal strip 6 in the finishing train 3. The data 102available at the output of the online monitor 9 preferably also containsreal-time model corrections.

Strip data 101 actually measured in the finishing train, and inparticular temperatures, will possibly not always be available andgenerally only at a few defined points, sometimes only at the pointsx_(A) and x_(E). Online adaptation 10 uses data 102 computed by theonline monitor 9, in particular temperatures determined by the onlinemonitor, as well as preferably measured temperatures 101.

With the aid of the online adaptation 10, correction factors aredetermined which are used in particular for correcting model errors inthe online monitor 9. Here, temperatures actually measured 101 arepreferably compared with calculated temperatures 102. The onlineadaptation 10 is linked both to the online monitor 9 and to the module11 for predicting the temperature of selected points on the strip.

Data originating from the output end of the online adaptation 10 ispreferably available at the input end of the module 1 for predicting thestrip temperature.

The module 11 can process further data determined by the online monitor9. The strip temperature calculated by the module 11 is passed on to thestrip temperature regulation 17. The module 11 for predicting the striptemperature also uses the strip temperature model of the module 12 fordetermining the strip temperature online.

Input variables of the strip temperature regulation 17 and of thelinearized model 15 are the actual temperature gradient determined bythe strip temperature model and a predetermined desired temperaturegradient. The desired temperature gradient is predetermined depending onthe plant type, the operating mode, the respective job and the desiredproperties of the metal strip 6.

The strip temperature regulation 17 uses input data 103 calculated bythe strip temperature model 12. Here, control specifications can be usedparticularly flexibly since the online monitor 9 can determine anyinterim temperature of the strip 6 inside the finishing train 3, even ifno appropriate measured values are available. FIG. 3 illustratesschematically problems relevant to model-predictive regulation, such asarise, for example, when metal in the ferrite-phase status range is tobe rolled. Besides the desired temperature indication T^(d) ₂ at the endx_(E) of the finishing train 3, further desired temperature values T^(d)₀, T^(d) ₁ inside the finishing train 3 are preferably used. If, forexample, the rolling operations of the first two rolling stands 3′ ofthe finishing train 3 are to occur in the austenite range, but theremaining rolling operations, i.e. the rolling operations of thedownstream rolling stands 3′, in the ferrite range, at least threedesired temperatures T^(d) ₀, T^(d) ₁, T^(d) ₂, as shown in FIG. 3, areneeded.

The first desired temperature T^(d) ₀ after the second rolling stand isto ensure that the temperature of the rolling operations in the firsttwo rolling stands lies above the transition temperature between thephase status ranges. The second desired temperature value T^(d) ₁ is toensure the phase transition before the third rolling stand of thefinishing train 3. If possible, a final temperature T^(d) ₂ at the endx_(E) of the finishing train 3 should also to be met.

The predicted temperatures needed T^(J) _(k=0,1,2) are provided by themodule 11 for predicting the strip temperature with the aid of a modelpreferably for multiple points P₀, P₁, P₂, on the strip. The striptemperature regulation 17 can also respond to short-term temperaturefluctuations that are caused, for example, by the furnace automaticcontrol. However, this preferably takes place as a result of a change inthe flow of the cooling agent 8 and not by a change in the strip speed vor in the flow of the material 16. Short-term temperature fluctuationsmay, for example, cause local unscheduled irregularities or folds in themetal strip 6.

Long-term temperature fluctuations, which may be caused, for example, bya rolling operation preceding the finishing train 3 and not shown indetail in the drawings, are preferably compensated for by acceleration aof the metal strip 6, i.e. by a change in the flow of the material 16.The prediction horizon 106 is adapted accordingly.

In order to solve the problem shown in FIG. 3, it is preferably solvedas a minimization problem with the aid of the linearized model 15. Tothis end, the control variables corresponding to the flow of thematerial 16 and the flow of the cooling agent 8 are preferably changedsuch that they minimize the weighted quadratic error of the predictedtemperatures T^(j) _(k=0,1,2) for the strip points P₀, P₁, P₂ withreference to the desired temperatures T^(d) _(k=0,1,2) (see equation I).Thus, at the individual valves 7, a coolant flow Q₀, Q₁ and Q₂, jointlyreferred to as 8, is effected which lies as far as possible from thetechnical limits of the inter-stand cooling devices 7, which arepreferably fashioned as coolant valves or water valves 7. In this way,the maximum possible tolerance is achieved at the inter-stand coolingdevices 7 so as later, i.e. in subsequent regulating steps, to be ableto respond to short-term temperature fluctuations.

The following adjustment limitations of the inter-stand cooling devices7 must be taken into consideration: the coolant flow Q₀, Q₁, Q₂ of avalve 7 can be changed only with a speed which matches the dynamics ofthe respective valve 7 and must not lie outside technically determinedminimum Q^(max) _(i) and maximum Q^(min) _(i) values. The flow of thematerial 16 must also lie within technical threshold values which aredetermined in particular by a maximum and a minimum speed of the metalstrip upon leaving the finishing train 3. As far as the flow of thematerial is concerned, a lower and an upper limit on the acceleration aof the metal strip 6 must also be observed.

A predicted temperature T^(j) _(k) for a given flow of the cooling agent8 and flow of the material 16 and for a given adaptation coefficient forthe regulating step concerned is calculated by the module 12 with theaid of the strip temperature model. The adaptation coefficient ispreferably frozen for further predictions. In order to calculate theadjustment variables for control for the next control steps, the currentflow of the cooling agent 8 and the current flow of the material 16 areset as a working point. The new predicted temperature T_(k) ^(j) canthen be expressed as T_(k) ^(j)+ΔT_(k) ^(j), the following applying:$\begin{matrix}{{{\Delta\quad T_{k}^{j}} = {\Delta\quad{T_{k}^{j}\left( {{\Delta\quad u_{i_{j}}^{j}},{\Delta\quad u_{i_{j + 1}}^{j}},{\ldots\quad\Delta\quad u_{\text{?}}^{j}},{\Delta\quad a},{\Delta\quad s}} \right)}}}{\text{?}\text{indicates text missing or illegible when filed}}} & (I)\end{matrix}$

Finally, the target function reproduced below in the variables Δu^(j)_(i), Δa and Δs, more details of which will be given in connection withFIGS. 5 and 6, is preferably solved, taking into account the adjustmentlimitations specified previously: $\begin{matrix}{{\sum\limits_{j = 0}^{J - 1}\quad{\sum\limits_{k = 0}^{K - 1}\quad{\frac{w_{k}^{j}}{2}{{T_{k}^{j} + {\Delta\quad T_{k}^{j}} - T_{k}^{d}}}^{2}}}} + {\frac{\delta}{2}{\sum\limits_{j = 0}^{J - 1}{\sum\limits_{i = i_{j}}^{{{\,^{i}k} - 1},j}{{{Q_{i}^{act} + {\Delta\quad u_{i}^{j}} - \frac{Q_{i}^{\max} + Q_{i}^{\min}}{2}}}^{2}\frac{\alpha}{2}{\sum\limits_{j = 0}^{J - 1}\quad{\sum\limits_{i = i_{j}}^{{{\,^{i}K} - 1},j}\quad{\frac{\Delta\quad u_{i}^{j}}{\Delta\quad t}}^{2}}}}}}} + {\frac{\beta}{2}{\frac{\Delta\quad a}{\Delta\quad t}}^{2}} + {\frac{\gamma}{2}{\frac{\Delta\quad s}{\Delta\quad t}}^{2}}} & ({II})\end{matrix}$

As FIG. 3 shows, the strip temperature is predicted into the futureuntil such time as a point on the strip P₀ reaches the last desiredtemperature value T^(d) ₂. As a rule, this lies at the end x_(E) of thefinishing train 3, where a pyrometer, not shown in detail in thedrawings, preferably measures the actual temperature of the metal strip6. The model-predictive prediction is carried out constantly forindividual regulating steps Δt.

FIGS. 4 and 5 illustrate the different adjustment horizon for the flowof the cooling agent (see FIG. 4) and for the flow of the material (seeFIG. 5). In both Figures, the abscissa represents a time axis.

The flow of the material 16 is preferably influenced by the strip speedv, the adjustment horizon preferably being restricted to a singleregulating step. Offset Δs and change in acceleration Δa are thenpreferably assumed to be constant (see FIG. 5). Short-term temperaturefluctuations, by contrast, are preferably influenced by the flow of thecooling agent Q_(j). For this, temperature prediction values arepreferably used for strip points P_(j) which, viewed in the direction offlow of the material, lie upstream of the corresponding inter-standcooling device 7, so that the strip points P_(j) do not reach thecorresponding inter-stand cooling device until the idle time 105 of thecorresponding valve 7 plus the computing time have expired.

Although the minimization (II) is carried out, taking into considerationall future coolant flow corrections Δu_(i) ^(j) (see FIG. 4) until theend of the setting horizon, the coolant flow Q^(act) _(ij) is updatedonly with the aid of the first correction Δu_(i) _(j) ^(j). In order toreduce possible oscillations, the updated values for Δu_(i) _(j) ^(j)Δaand Δs are where applicable multiplied with a relaxation factor 0<χ≦1.

Minimizing the equation (II) taking into account the correspondingadjustment limitations, especially those mentioned previously, meanssolving a non-linear programming problem which is as a rule extremelycomputation-intensive and which, in order to be online-capable, has tobe accelerated. Regulating steps Δt can, according to the invention, becarried out, for example, every 200 milliseconds.

In order to achieve an acceleration, the procedure followed ispreferably analogous to the Gauss-Newton method and linearizes thepredicted temperature change about the working point: $\begin{matrix}{{\Delta\quad T_{k}^{j}} \approx {{\sum\limits_{i = i_{j}}^{t_{ki}}{S_{ki}^{j}\Delta\quad u_{i}^{j}}} + {{\overset{\sim}{S}}_{k}^{j}\Delta\quad a} + {{\overset{\_}{S}}_{k}^{j}\Delta\quad s}}} & ({III})\end{matrix}$

The sensitivities S_(ki) ^(j), {tilde over (S)}_(k) ^(j) and {overscore(S)}_(k) ^(j) are approximated by finite differences as follows:$\begin{matrix}{S_{k,i_{j}}^{j} = \frac{T_{k}^{j}{_{Q_{ij}^{act} + \Delta}{- T_{k}^{j}}}_{Q_{ij}^{act}}}{\Delta}} & ({IV})\end{matrix}$ $\begin{matrix}{{\overset{\sim}{S}}_{k}^{j} = \frac{T_{k}^{0}{_{a^{act} + \Delta}{- T_{k}^{0}}}_{a^{act}}}{\Delta}} & (V) \\{{\overset{\_}{S}}_{k}^{j} = \frac{T_{k}^{0}{_{{h_{exit}v_{exit}^{act}} + \Delta}{- T_{k}^{0}}}_{v_{exit}v_{exit}^{act}}}{\Delta}} & ({VI})\end{matrix}$

In order to determine the sensitivities S_(ki) ^(j), {tilde over(S)}_(k) ^(j) and {overscore (S)}_(k) ^(j), the strip temperature model,in addition to the prediction of the temperature T^(j) _(k), has to besolved once again. According to the Gauss-Newton method, thelinearization (III) is inserted in the quadratic error of the targetfunction (II). The following approximation is produced: $\begin{matrix}{{{T_{k}^{j} + {\Delta\quad T_{k}^{j}} - T_{k}^{d}}}^{2} \approx {{{T_{k}^{j} - T_{k}^{d}}}^{2} + {2\left( {T_{k}^{j} - T_{k}^{d}} \right){\sum\limits_{i = i_{j}}^{i_{kj}}{S_{ki}^{j}\Delta\quad u_{i}^{j}}}} + {2\left( {T_{k}^{j} - T_{k}^{d}} \right){\overset{\sim}{S}}_{k}^{j}\Delta\quad a} + {2\left( {T_{k}^{j} - T_{k}^{d}} \right){\overset{\_}{S}}_{k}^{j}\Delta\quad s} + {2{\overset{\sim}{S}}_{k}^{j}\Delta\quad a{\sum\limits_{i = i_{j}}^{i_{kj}}{S_{ki}^{j}\Delta\quad u_{i}^{j}}}} + {2{\overset{\_}{S}}_{k}^{j}\Delta\quad s{\sum\limits_{i = i_{j}}^{i_{kj}}{S_{ki}^{j}\Delta\quad u_{i}^{j}}}} + {2{\overset{\_}{S}}_{k}^{j}{\overset{\sim}{S}}_{k}^{j}\Delta\quad s\quad\Delta\quad a} + {\sum\limits_{i = i_{j}}^{i_{kj}}{\sum\limits_{i = i_{j}}^{i_{kj}}{S_{ki}^{j}S_{ki}^{j}\Delta\quad u_{i}^{j}\Delta\quad u_{i}^{j}}}} + {{{\overset{\sim}{S}}_{k}^{j}}^{2}{{\Delta\quad a}}^{2}} + {{{\overset{\_}{S}}_{k}^{j}}^{2}{{\Delta\quad s}}^{2.}}}} & ({VII})\end{matrix}$

If the right-hand side of (VII) is now inserted in (II), then thequadratic programming problem presents itself in the following form:$\begin{matrix}{\min = {f + {{\underset{\_}{g}}^{t}\underset{\_}{\chi}} + {\frac{1}{2}\underset{\_}{\chi^{t}\underset{\_}{H}\chi}}}} & ({VIII}) \\{{\underset{\_}{b}}^{lower} \leq \underset{\_}{\chi} \leq {\underset{\_}{b}}^{upper}} & ({IX})\end{matrix}$

Here f is a scalar, H a symmetrical, positive semi-definite N×N matrixwhich is positively definite when the positive parameters α, β and γ arechosen sufficiently large. The remaining variables are n-dimensionalcolumn vectors. The inequality (IX) is to be understood in componentterms.

In order to solve the quadratic optimization problem, an active-setstrategy is preferably used.

According to the invention, in particular travel diagrams for therolling speed v and/or for the water ramps or coolant ramps of theinter-stand cooling (7) are particularly advantageously calculated andmatched with especially high precision.

In addition to the advantages of the invention hereinabove andespecially described in the introduction, the invention enables for thefirst time in the control and/or regulation of the temperature of ametal strip 6 in a simple manner a different weighting, in the sense ofa prioritization, of the indications relevant for said control.

According to the invention, a flexible controlling and regulating methodis provided which can also be used for other plant parts such as e.g. inparticular the roughing train 2 or else the cooling stretch 4. A use ofthe invention covering more than one part of the plant 1 to 5 ispossible. Use of the invention is particularly advantageous indual-phase rolling and in the travel of a thickness wedge during therolling of a semi-continuous slab.

1-15. (canceled)
 16. A method of controlling a temperature of stripmetal processed in a finishing train of a technical installation, themethod comprising: comparing a target temperature gradient to an actualtemperature gradient associated with the strip metal, the actualtemperature gradient including a point temperature gradient determinedfor a number of individual local points of the strip metal; anddetermining a target function for at least one actuator arranged in thefinishing train based on the target temperature gradient, the actualtemperature gradient, and the point temperature gradient for adjustingthe actuator and controlling the temperature, wherein the calculatedtarget function adheres to side conditions related to operatingconstraints of the technical installation.
 17. The method according toclaim 16, wherein adjusting signals for adjusting the actuator arecalculated by solving an optimization problem represented by the targetfunction and the side conditions.
 18. The method according to claim 17,the optimization problem includes linear side conditions.
 19. The methodaccording to claim 18, wherein the optimization problem is solved basedon an active set strategy.
 20. The method according to claim 18, whereinthe optimization problem is a quadratic optimization problem.
 21. Themethod according to claim 17, wherein the optimization problem is solvedonline.
 22. The method according to claim 17, wherein at least one ofthe adjusting signals is used for controlling a flow of a cooling agent.23. The method according to claim 17, wherein at least one of theadjusting signals is used for controlling a material flow of the stripmetal through the finishing train.
 24. The method according to claim 16,wherein the target function includes a desired end temperature of thestrip metal at an end of the finishing train.
 25. The method accordingto claim 16, wherein the target function includes at least one desiredprocess temperature of the strip meal within the finishing train. 26.The method according to claim 16, wherein the actual temperaturegradient is obtained from at least one mathematical model describing thestrip metal's processing in the finishing train.
 27. The methodaccording to claim 26, wherein the mathematical model is adapted online.28. The method according to claim 16, further comprising pre-calculatingan online-capable pass schedule algorithm using a non-linearoptimization problem including further side conditions.
 29. The methodaccording to claim 28, wherein the further side conditions aresubstantially identical to the side conditions.
 30. A computer readablemedium, comprising program code for executing a method of controlling atemperature of strip metal processed in a finishing train of a technicalinstallation, the program code designed to: compare a target temperaturegradient to an actual temperature gradient associated with the stripmetal, the actual temperature gradient including a point temperaturegradient determined for a number of individual local points of the stripmetal; and determine a target function for at least one actuatorarranged in the finishing train based on the target temperaturegradient, the actual temperature gradient, and the point temperaturegradient for adjusting the actuator and controlling the temperature,wherein the calculated target function adheres to side conditionsrelated to operating constraints of the technical installation.
 31. Acomputing device for controlling a temperature of strip metal processedin a finishing train of a technical installation, the computing devicecomprising a processing unit configured to execute a software program,wherein the software program is designed to: comparing a targettemperature gradient to an actual temperature gradient associated withthe strip metal, the actual temperature gradient including a pointtemperature gradient determined for a number of individual local pointsof the strip metal; and determine a target function for at least oneactuator arranged in the finishing train based on the target temperaturegradient, the actual temperature gradient, and the point temperaturegradient for adjusting the actuator and controlling the temperature,wherein the calculated target function adheres to side conditionsrelated to operating constraints of the technical installation.
 32. Thecomputing device according to claim 31, further comprising: acalculating module for determining the actual temperature gradient ofthe metal strip online using a mathematical model describing the stripmetal's processing in the finishing train; and a control module forcontrolling the temperature of the metal strip using the targetfunction.